Noun
Laplacian matrix (plural Laplacian matrices)
(graph theory) A square
n
×
n
{\displaystyle n\times n}
matrix which describes an undirected graph of
n
{\displaystyle n}
vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices.
The Laplacian matrix is a modified form of the adjacency matrix that incorporates information about the degrees of the vertices, and is useful in some calculations such as Kirchhoff's theorem on the number of spanning trees of a graph. Source: Internet